Problem: Multiply and simplify the following complex numbers: $({2-2i}) \cdot ({4-4i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2-2i}) \cdot ({4-4i}) = $ $ ({2} \cdot {4}) + ({2} \cdot {-4i}) + ({-2i} \cdot {4}) + ({-2i} \cdot {-4i}) $ Then simplify the terms: $ (8) + (-8i) + (-8i) + (8i^2) $ Imaginary unit multiples can be grouped together. $ 8 + (-8 - 8)i + 8 i^2 $ After we plug in $i^2 = -1$, the result becomes $ 8 + (-8 - 8)i - 8 $ The result is simplified: $ (8 - 8) + (-16i) = -16i $